Abstract
Compliant mechanism mainly relies on large deformations of compliant rods to transmit motions, forces and energy. The geometric nonlinearity of the compliant rods is one of the most serious challenges when accurate modeling and dynamic simulation are performed. The absolute nodal coordinate formulation (ANCF) and geometrically exact beam theory (GEBT) are employed to investigate the nonlinear modeling and analysis of compliant mechanisms in this paper. By taking account of deformation characteristics of the compliant rod at the external connection, a new ANCF beam element with one nodal deformation constraint is proposed. Based on the locking alleviation technique, strain split method, the effect of the locking phenomenon of the ANCF beam element on the dynamic simulation of compliant mechanism is investigated. In comparison, the Euler-Bernoulli beam element, which is a kind of locking free GEBT element, is also used for the dynamic analysis of the compliant mechanism. Finally, the numerical example of a partial compliant four-bar mechanism is presented to illustrate the accuracy and effectiveness of ANCF and GEBT beam elements for the dynamic problems of compliant mechanisms.
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Howell, L.L.: Compliant Mechanisms. Wiley, New York (2001)
Midha, A., Howell, L.L., Norton, T.W.: Limit positions of compliant mechanisms using the pseudo-rigid-body model concept. Mech. Mach. Theory 35(1), 99–115 (2000)
Howell, L.L., Midha, A.: A method for the design of compliant mechanisms with small-length flexural pivots. J. Mech. Des. 116, 280–290 (2008)
Howell, L.L., Midha, A., Norton, T.W.: Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms. J. Mech. Des. 118, 126–131 (2008)
Wang, W., Bi, S., Zhang, L.G.: Dynamic modeling of compliant mechanisms based on 2R pseudo-rigid-body model. Appl. Mech. Mater. 163, 277–280 (2012)
Yu, Y., Zhu, S.: 3R1H pseudo-rigid-body model for compliant mechanisms with inflection beams, pp. 39–47 (2018)
Shabana, A.A.: An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Tech. Rep. MBS96-1-UIC, Dept of Mechanical Engineering, Univ of Illinois at Chicago (1996)
Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49(1), 55–70 (1985)
Simo, J.C., Vu-Quoc, L.: A three-dimensional finite-strain rod model. Part II: computational aspects. Comput. Methods Appl. Mech. Eng. 58(1), 79–116 (1986)
Crisfield, M.A., Jelenic, G.: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. R. Soc. London. Ser. A: Math., Phys. Eng. Sci. 455(1983), 1125–1147 (1999)
Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, Cambridge (2013)
Shabana, A.A.: Computational Continuum Mechanics, 3rd edn. Wiley, Chichester (2018)
Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. J. Mech. Des. 123(4), 614 (2002)
Shabana, A.A., Yakoub, R.Y.: Three dimensional absolute nodal coordinate formulation for beam elements: theory. J. Mech. Des. 123(4), 606 (2002)
Zhang, Z., Qi, Z., Wu, Z., et al.: A spatial Euler-Bernoulli beam element for rigid-flexible coupling dynamic analysis of flexible structures. Shock. Vib. 2015, 1–15 (2015)
Patel, M., Shabana, A.A.: Locking alleviation in the large displacement analysis of beam elements: the strain split method. Acta Mech. 229(7), 2923–2946 (2018)
Nachbagauer, K.: State of the art of ANCF elements regarding geometric description, interpolation strategies, definition of elastic forces, validation and the locking phenomenon in comparison with proposed beam finite elements. Arch. Comput. Methods Eng. 21(3), 293–319 (2014)
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This research was supported by the financial support of the National Natural Science Foundation of China (Grants no. 11602228).
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Zhang, Z., Zhou, X., Fang, Z. (2020). Dynamic Analysis of Compliant Mechanisms Using Absolute Nodal Coordinate Formulation and Geometrically Exact Beam Theory. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_26
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DOI: https://doi.org/10.1007/978-3-030-23132-3_26
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